Very creative. The only problem I find is the fine paper fins, as they would bend while going down, causing the rocket to fly in a problematic angle. And the wooden frame catching fire if something drastically weird happens. You could just put a guide for the nail to go in 90 degrees, and make a butt-cap for it(instead of using hammer, just bash it in with a hard steel cylinder that attaches to the back and slides back and forth).
Looking for an Age Verifier who passes through Renfrew area to contact me! PM me please!